January 25, 2005

Applied Auction Theory

I was at a charity benefit auction in early December. The was a professional auctioneer running the
bidding and he was absolutely amazing. Aside from his amazing sense for the “micro-tactical” issues of running
an auction -- knowing what to say, when to pause, when to egg someone one, etc.
-- he was also changing up the type of auction based on the item up for bid.

The fancy name for the most common type of auction is
“open-outcry, second price.” The
open-outcry is pretty clear (as opposed to a sealed-bid or some other means of
signaling such as eBay) but the second price part is a little more subtle. Imagine an auction where just two people are
bidding, me and you. I’m willing to pay
up to $20 (my “reservation price”) for an item and you are willing to pay
$30. You will win the item for the
minimum bid increment above $20, since that is above my reservation price of
$20 – thus the seller gets the second highest price. This should be familiar to anyone who has
ever used eBay.

Another type of auction is a Dutch auction. This type of auction is a first-price
auction, and is named after the Dutch because they invented this auction as a
way to sell large lots of tulips. The
price starts very high and is gradually lowered. To use the example from above, where my
reservation price is $20 and yours is $30, the auctioneer might start the first
bid at $100. The price is then lowered
until someone bids, who then wins the item. In this case, you would win the item and pay your reservation price of
$30, which is the highest amount that anyone was willing to bid.

There are other interesting variations on this auction, such
as the reverse Dutch auction which is useful when auctioning off large numbers
of identical items. Many universities
use reverse Dutch auctions to efficiently allocate "scarce resources" such as
seats in popular classes. W. R. Hambrecht & Company is an investment bank specializes in IPOs using reverse Dutch
auctions. The best known Dutch auction
in recent memory was the Google IPO.

During one of the auctions the auctioneers did something
absolutely brilliant. The item up for
bid was a week in an apartment in Barcelona, Spain. The apartment is nicely furnished, near a large
market, near public transportation and the buyer could pick any week this
summer. The bidding opened at $1,000 and
was quickly bid up past $2,500. In the
end there were three bidder remaining. Bidders B and C had simultaneously put their paddles up for $2,900. When the price was raised to $3,000, there
was silence, and then bidder A, put up his paddle. Once, twice, sold for $3,000 to bidder A.

The auctioneer interrupted the applause, “Hold on, hold
on. I’m going to do something a little
crazy here” To bidder B: “Would you pay
$2,900 for another week in this apartment in Barcelona?” Bidder B said yes. To bidder C: “Would you pay $2,900 for a third
week in this apartment in Barcelona?” Bidder C said yes. To bidder A:
“You know what, I’m going to give you your week in the apartment for $2,900.”

Once the dust settled, the auctioneer had sold three weeks
in an apartment in Barcelona for $2,900 x 3 = $8,700! The auctioneer knew all along that he had
three weeks to sell, but he kept this information to himself and let the
auction proceed as if there was only the one week.

If he had auctioned off a single, three week block of time
in the apartment, my guess is that it would have gone for much less. Conversely, if he had announced that there are
three, one week slots in this apartment, it would have changed the dynamics of
the auction, and likely ruined the unique nature of the item.

Not to get too technical, but one could argue that he simply
sold three items at the “third price” of $2,900, since $3,000 was the second
price. This is true, but I would argue that
the competition among the bidders would not have been as intense if three
separate actions had been held. These
were not particularly experienced bidders, and I would guess that they
increased their reservation price as the auction heated up.